9 problems

Let $\mathbb{L}_{SO}^\otimes$ be the proposed oriented $\infty$-operad, and let $\Omega^2\operatorname{Bord}_3^{SO}$ be the symmetric monoidal $\infty$-category of oriented 3-dimen…

Harpaz's conjecture. The functor $N_{\mathrm{Lurie}}$ induces an equivalence of $\infty$-categories after localizing at weak equivalences.

Let $G$ be a finite group, let $(\operatorname{sOp}^{\operatorname{col}})^G$ be the category of $G$-objects in simplicial coloured operads, and let $G$-$\infty$-$\operatorname{Op}$…

Let $({\mathscr{O}},{\mathscr{T}})$ be an orbital pair, let $\Delta_{({\mathscr{O}},{\mathscr{T}})}^{\operatorname{op}}$ be its associated algebraic pattern, and let…

Let $\text{Fin}^{\text{op}}$ be the opposite category of finite sets, and let $\text{Burn}^{\text{eff}}$ denote the effective Burnside 2-category, or spans of finite sets. A cyclic…

Biran–Cornea identification conjecture. The categories $T^s$ of Biran and Cornea are the discrete colored planar operads associated to the $s$-dot constructions of…

Paracyclic compatibility conjecture. The map is compatible with the paracyclic action on the $s$-dot construction.

Compatibility conjecture. The filtration of the vertical-collar theorem defines a map of colored planar $\infty$-operads to the colored planar $\infty$-operad obtained from the $s$…

Let $\mathcal{X} \to \Delta^{\operatorname{op}}$ be an admissible double $\infty$-category and let $\mathcal{V}$ be a presentably monoidal $\infty$-category. Corollary 3.?? equips…